Prove the following identities: ^2 + cosec^2 = ^2 cosec^2 . - Vidyadip

Question

Prove the following identities: $\sec^2\theta + cosec^2\theta = \sec^2\theta\ cosec^2\theta $.

✓

Answer

LHS = $\sec^2\theta + cosec^2\theta$
$=\frac{1}{\cos ^2 \theta}+\frac{1}{\sin ^2 \theta}$
$=\frac{\sin ^2 \theta+\cos ^2 \theta}{\sin ^2 \theta \cdot \cos ^2 \theta}$
$=\frac{1}{\sin ^2 \theta \cdot \cos ^2 \theta}$
$=\frac{1}{\sin ^2 \theta} \times \frac{1}{\cos ^2 \theta}$
$= \sec^2\theta\ cosec^2\theta$
= RHS
Hence proved.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "[2 Mark Question Answer]" from Trigonometry→Trigonometry — all question types→Mathematics STD 10 question papers→ICSE Board STD 10 question papers→ICSE Board question paper generator→

Similar questions

Prove. $cosec^4A - cosec^2 A = \cot^4 A + \cot^2 A$

Find the locus of the centre of a circle of radius r touching externally a circle of radius R.

An aeroplane travelled a distance of 400 km at an average speed of x km/hr. On the return journey the speed was increased by 40 km/hr. Write down the expression for the time taken for
The outward journey

Perform the following operation and state the single transformation that take place :
$M_x. M_o$ on $P (-1,-3)$

Find the image of the point A$(5,3)$ under reflection in the point P$(-1,3).$

Suppose the pen drawn in (i) is defective and is not replaced. Now one more pen is drawn at random from the rest. What is the probability that this pen is:
a) defective
b) not defective?

A card is drawn from a well shuffled pack of 52 cards. Find the probability that the card drawn is: a red card

Find without division, the remainder in the following:
$2x^3 - 3x^2 + 6x - 4$ is divisible by $(2x-3)$

Find $A,$ if $0^\circ \leq A \leq 90^\circ$ and $2cos^2A - 1 = 0$

Solve for x : 3 - 2x ≥ x - 12, x ∈ N